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4. (6 points) Let {X1, ..., X2n} denote a random sample from a population with mean u and variance 1. Consider the following estimators of

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4. (6 points) Let {X1, ..., X2n} denote a random sample from a population with mean u and variance 1. Consider the following estimators of M: 2n 1 M1 = 2n Exi i=1 n 12 = - n . Exi i=1 X2n 1 2n 1 MA = 2n Xit 2n i=1 (a) Find all the unbiased estimators of M. (b) Calculate the variance of all estimator. Which estimator is the most efficient one? (c) Find all the consistent estimators of M

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